Liouvillian Integrability and the Poincaré Problem for Nonlinear Oscillators with Quadratic Damping and Polynomial Forces

Demina, Maria V.; Кузнецов, Н. С.

doi:10.1007/s10883-020-09513-2

Cited by 6 publications

(1 citation statement)

References 25 publications

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“…is has prompted researchers into the study of nonlinear dynamical systems [1][2][3]. Typically, a nonlinear system is regarded as a system in which the laws governing the time evolution of its state variables depend on the values of these variables in a manner that deviates from proportionality [4].…”

Section: Introductionmentioning

confidence: 99%

FPGA Realization of Spherical Chaotic System with Application in Image Transmission

Nuñez-Perez

Adeyemi

Sandoval-Ibarra³

et al. 2021

Mathematical Problems in Engineering

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This paper considers a three-dimensional nonlinear dynamical system capable of generating spherical attractors. The main activity is the realization of a spherical chaotic attractor on Intel and Xilinx FPGA boards, with a focus on implementation of a secure communication system. The first major contribution is the successful synchronization of two chaotic spherical systems, in VHDL program, in a master-slave topology using Hamiltonian forms. The synchronization errors show that the two spherical chaotic systems synchronize in a very short time after which the error signals become zero. The second major contribution is the FPGA realization of a spherical chaotic attractor-based secure communication system, which involves encrypting both grayscale and RGB images with chaos and diffusion key at the transmitting system, sending the encrypted image via the state variables, and reconstructing the encrypted image at the receiving system. The Intel Stratix III and Xilinx Artix-7 AC701 results are the same as those of MATLAB. The statistical analyses of the encrypted and received images show that the implemented system is very effective, as it reveals high degree of randomness in the encrypted images with the entropy test, and the obtained correlation coefficient, which is zero, removes relativity between the original and encrypted images. Finally, the transmission system fully recovers the original grayscale and RGB images without loss of information.

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Section: Introductionmentioning

confidence: 99%

FPGA Realization of Spherical Chaotic System with Application in Image Transmission

Nuñez-Perez

Adeyemi

Sandoval-Ibarra³

et al. 2021

Mathematical Problems in Engineering

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Oscillations of a Vehicle Equipped with Hydraulic Shock Absorbers

Marinca

Tudor

2022

Springer Proceedings in Physics

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Energy analysis of Duffing oscillators with quadratic damping: exact solutions

Rakarić

Kovacic

2021

J. Phys.: Conf. Ser.

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Oscillators with a Duffing-type restoring force and quadratic damping are dealt with in this paper. Four characteristic cases of this restoring force are analysed: hardening, softening, bistable and a pure cubic one. Their energy-displacement relationships are considered, and the corresponding closed-form exact solutions are obtained in terms of the incomplete Gamma function, which represent new results. Such results provide insight into damped dynamics of the class of system, including finding the phase trajectories as well as the comparison between these cases from the viewpoint of the energy loss per cycle.

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Liouvillian Integrability and the Poincaré Problem for Nonlinear Oscillators with Quadratic Damping and Polynomial Forces

Cited by 6 publications

References 25 publications

FPGA Realization of Spherical Chaotic System with Application in Image Transmission

FPGA Realization of Spherical Chaotic System with Application in Image Transmission

Oscillations of a Vehicle Equipped with Hydraulic Shock Absorbers

Energy analysis of Duffing oscillators with quadratic damping: exact solutions

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